This is a first-year course which is part of a sequence of two consecutive courses.
In this course, we will cover the main topics in Linear Algebra: Algebra of matrices, linear systems of equations, vector spaces, linear independence, basis and dimension, infinite-dimensional vectors spaces, linear transformations, matrix representation, isomorphisms, quotient spaces, dual spaces, and determinants.
The language and concepts of matrix theory and, more generally, of linear algebra have come into widespread usage in the social and natural sciences, computer science, and statistics. In addition, linear algebra continues to be of great importance in modern treatments of geometry and analysis.
Friedberg, S. H., Insel, A. J., Spence, L. E., Linear Algebra, 4th ed. Prentice Hall